# Closure, Interior and limit points of finite compliment topology question

• Apr 8th 2009, 04:28 PM
monkey.brains
Closure, Interior and limit points of finite compliment topology question
Hey

I was wondering if someone could help me out with the following question.

Let U be any open set in the finite complement topology on $\Re$.

(a)Describe the Cl(U), Int(U) and $\mathfrak{d}$(U)

(b) What is the set of limit points of U
• Apr 8th 2009, 10:14 PM
aliceinwonderland
Quote:

Originally Posted by monkey.brains
Hey

I was wondering if someone could help me out with the following question.

Let U be any open set in the finite complement topology on $\Re$.

(a)Describe the Cl(U), Int(U) and $\mathfrak{d}$(U)

(b) What is the set of limit points of U

(a) Cl(U) = R, Int(U) = U,
$\mathfrak{d}$ $(U) = \bar{U} \cap \overline{R\setminus U}$,
Since U is an open set, $\mathfrak{d}$(U) = $\overline{R\setminus U} = R \setminus U$.
(b)The limit points of U are all points in R.
• Apr 10th 2009, 02:47 PM
monkey.brains
Quote:

Originally Posted by aliceinwonderland
(a) Cl(U) = R, Int(U) = U,
$\mathfrak{d}$ $(U) = \bar{U} \cap \overline{R\setminus U}$,
Since U is an open set, $\mathfrak{d}$(U) = $\overline{R\setminus U} = R \setminus U$.
(b)The limit points of U are all points in R.

hey could you please clarify what does the line over R minus U means??
• Apr 10th 2009, 02:53 PM
Plato
Quote:

Originally Posted by monkey.brains
hey could you please clarify what does the line over R minus U means??

Often $\overline{A}$ stands for the closure of $A$.